Fermilab

I don't know weather you can help me but one thing that i have been interested in for the past several years is how the mass of a particle so small can be measured and i was hopeing you might be able to help me.

thank you,
jeff kirkwood

Dear Jeff,

A very interesting question. Obviously, we can't just put a subatomic particle on a balance and weigh it. Actually R.A.Millikan did an experiment early in the century where the electric charge to mass ratio of an electron was measured by charging droplets of oil and then observing how they fell under the influence of gravity acting on the mass and then rose under the pull of an external electric field acting on the charge.

Anyway, these days, subatomic particles are created with huge speeds. There is a difference between the energy of a particle and the momentum of a particle though. When the speed is very fast (relativistic speeds), the formula:

Energy = sqrt( (momentum*c)² + (mass*c²)² )

must be used although it can be used at lower speeds also. (Energy = kinetic energy + mass*c²) where c = speed of light.

So E = E_kin+ mc².

A charged particle's momentum is routinely measured by exploiting the fact that it bends in a magnetic field inversely proportional to the momentum. You can bend the particle and measure how much it deflects with a known magnetic field and magnet length.

The kinetic energy can be measured by letting a particle (charged or neutral) slam into a piece of the appropriate material. If there is enough of the material, the particle will stop leaving all its kinetic energy in the material. If it is an antiparticle, it may annihilate and leave its rest mass energy (mc²) in the material as well.

One can solve the equation (c = 1) for the mass:

(E_kin + m)² - p² = m²

or

m² - 2*m*E_kin + (p² - E_kin²) = 0

The appropriate material can be a gas-filled proportional wire chamber (for charged particles) or scintillator (for either depending on the type of scintillator). For example, scintillator emits near-visible light when a particle passes through. The light can be sensed by a commercially available photomultiplier tube (or in some cases, a photodiode will do). A wire chamber is filled with an appropriate gas. When a particle passes through, electrons are created from ionizations of the gas atoms. A high voltage is applied to the wires such that the electrons (being electrically charged) are pulled towards the wire. This produces a current at the output electrodes of the chamber.

The energy of neutrons can be measured by other types of scintillator material but the fundamental interactions are by the nuclear strong force since the neutron has no electric charge.

Actually most composite particles decay to other particles. Thus many neutral particles will decay into charged particles whose momentum can be measured so the mass of the neutral particle can be reconstructed. Another way of doing this is to measure the energies of the decay particles and also measure their angles relative to the original particle direction. One can reconstruct the mass of the original particle this way. One must know the original momentum of the beam of original particles though is as the case when you use a primary beam at some storage ring.

So basically, in particle physics, one usually measures the energy and momentum and infers the mass.

Glenn Blanford
Physicist (graduate student)
with University of California, Irvine

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